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- Integrate by partial fractions
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Rewrite the fraction $\frac{x^3+3x^2-3x-7}{\left(x^2+1\right)\left(x-1\right)\left(x-2\right)}$ in $3$ simpler fractions using partial fraction decomposition
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$\frac{-\frac{17}{5}x+\frac{1}{5}}{x^2+1}+\frac{3}{x-1}+\frac{7}{5\left(x-2\right)}$
Learn how to solve problems step by step online. Find the integral int((x^3+3x^2-3x+-7)/((x^2+1)(x-1)(x-2)))dx. Rewrite the fraction \frac{x^3+3x^2-3x-7}{\left(x^2+1\right)\left(x-1\right)\left(x-2\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-\frac{17}{5}x+\frac{1}{5}}{x^2+1}+\frac{3}{x-1}+\frac{7}{5\left(x-2\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-\frac{17}{5}x+\frac{1}{5}}{x^2+1}dx results in: -\frac{17}{10}\ln\left(x^2+1\right)+\frac{1}{5}\arctan\left(x\right). The integral \int\frac{3}{x-1}dx results in: 3\ln\left(x-1\right).
